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NASA NTRS2011

TPSAS-NF1676L-12263-DND

The increasing presence of airport surface surveillance technologies has spawned a strong interest in airport surface traffic management research; the vast majority has assumed that the airport’s runway configuration is known and constant. Tactical Runway Configuration Management (TRCM), one component of NASA’s System Oriented Runway Management concept, plans the airport configuration to optimize traffic efficiency for the forecast weather, traffic, and other factors. While planning runway configuration can provide benefit and is required by other automation concepts, larger benefits are possible by planning other airport configuration decisions, such as runway assignment policies, that are currently made manually by controllers. A laboratory prototype of the TRCM algorithm which selects optimal airport configuration schedules has been implemented and studied within a simulation environment. The presentation will describe simulation results for several airports, under various weather and traffic conditions. The sequence of airport configurations recommended by TRCM result in significantly less delay than the airport configurations that were actually used by controllers, illustrating both the potential benefit from airport configuration optimization and the ability of TRCM to provide effective airport configuration schedules. The application to several, distinct airports demonstrates the approach is capable of handling the differences between airports with a common algorithm, while providing decision support that respects the current procedures at those airports. Consequently, TRCM is able to be deployed to any airport within the current National Airspace System. The TRCM algorithmic approach is also extensible to future operational scenarios. NASA is in the process of transferring the initial TRCM technology to the FAA. Future research will extend the concept and algorithm to provide coordinated plans for metroplex airports and study NextGen applications.

Stephen Atkins↗

NASA NTRS2013

Experiment Description and Results for Arrival Operations Using Interval Management with Spacing to Parallel Dependent Runways (IMSPiDR)

The predicted increase in the number of commercial aircraft operations creates a need for improved operational efficiency. Two areas believed to offer increases in aircraft efficiency are optimized profile descents and dependent parallel runway operations. Using Flight deck Interval Management (FIM) software and procedures during these operations, flight crews can achieve by the runway threshold an interval assigned by air traffic control (ATC) behind the preceding aircraft that maximizes runway throughput while minimizing additional fuel consumption and pilot workload. This document describes an experiment where 24 pilots flew arrivals into the Dallas Fort-Worth terminal environment using one of three simulators at NASA?s Langley Research Center. Results indicate that pilots delivered their aircraft to the runway threshold within +/- 3.5 seconds of their assigned time interval, and reported low workload levels. In general, pilots found the FIM concept, procedures, speeds, and interface acceptable. Analysis of the time error and FIM speed changes as a function of arrival stream position suggest the spacing algorithm generates stable behavior while in the presence of continuous (wind) or impulse (offset) error. Concerns reported included multiple speed changes within a short time period, and an airspeed increase followed shortly by an airspeed decrease.

Baxley, Brian T.↗

NASA NTRS2013

Evaluation of the Terminal Area Precision Scheduling and Spacing System for Performance-Based Navigation Arrivals

The growth of global demand for air transportation has put increasing strain on the nation's air traffic management system. To relieve this strain, the International Civil Aviation Organization has urged all nations to adopt Performance-Based Navigation (PBN), which can help to reduce air traffic congestion, decrease aviation fuel consumption, and protect the environment. NASA has developed a Terminal Area Precision Scheduling and Spacing (TAPSS) system that can support increased use of PBN during periods of high traffic, while supporting fuel-efficient, continuous descent approaches. In the original development of this system, arrival aircraft are assigned fuel-efficient Area Navigation (RNAV) Standard Terminal Arrival Routes before their initial descent from cruise, with routing defined to a specific runway. The system also determines precise schedules for these aircraft that facilitate continuous descent through the assigned routes. To meet these schedules, controllers are given a set of advisory tools to precisely control aircraft. The TAPSS system has been evaluated in a series of human-in-the-loop (HITL) air traffic simulations during 2010 and 2011. Results indicated increased airport arrival throughput up to 10 over current operations, and maintained fuel-efficient aircraft decent profiles from the initial descent to landing with reduced controller workload. This paper focuses on results from a joint NASA and FAA HITL simulation conducted in 2012. Due to the FAA rollout of the advance terminal area PBN procedures at mid-sized airports first, the TAPSS system was modified to manage arrival aircraft as they entered Terminal Radar Approach Control (TRACON). Dallas-Love Field airport (DAL) was selected by the FAA as a representative mid-sized airport within a constrained TRACON airspace due to the close proximity of a major airport, in this case Dallas-Ft Worth International Airport, one of the busiest in the world. To address this constraint, RNAV routes and Required Navigation Performance with the particular capability known as Radius-to-Fix (RNP-RF) approaches to a short final were used. The purpose of this simulation was to get feedback on how current operations could benefit with the TAPSS system and also to evaluate the efficacy of the advisory tools to support the broader use of PBN in the US National Airspace System. For this NASA-FAA joint experiment, an Air Traffic Control laboratory at NASA Ames was arranged to simulate arrivals into DAL in Instrument Meteorological Conditions utilizing parallel dependent approaches, with two feeder positions that handed off traffic to one final position. Four FAA controllers participated, alternately covering these three positions. All participants were Full-Performance Level terminal controllers and members of the National Air Traffic Controllers Association. During the simulation, PBN arrival operations were compared and contrasted in three conditions. They were the Baseline, where none of the TAPSS systems TRACON controller decision support advisories were provided, the Limited Advisories, reflecting the existing but dormant capabilities of the current terminal automation equipment with providing a subset of the TAPSS systems advisories; numerical delay, landing sequence, and runway assignment information, and the Full Advisories, with providing the following in addition to the ones in the Limited condition; trajectory slot markers, timelines of estimated times of arrivals and sched

Performance based navigation↗

NASA NTRS2011

Evaluation of an Airborne Spacing Concept, On-Board Spacing Tool, and Pilot Interface

The number of commercial aircraft operations is predicted to increase in the next ten years, creating a need for improved operational efficiency. Two areas believed to offer significant increases in efficiency are optimized profile descents and dependent parallel runway operations. It is envisioned that during both of these types of operations, flight crews will precisely space their aircraft behind preceding aircraft at air traffic control assigned intervals to increase runway throughput and maximize the use of existing infrastructure. This paper describes a human-in-the-loop experiment designed to study the performance of an onboard spacing algorithm and pilots ratings of the usability and acceptability of an airborne spacing concept that supports dependent parallel arrivals. Pilot participants flew arrivals into the Dallas Fort-Worth terminal environment using one of three different simulators located at the National Aeronautics and Space Administration s (NASA) Langley Research Center. Scenarios were flown using Interval Management with Spacing (IM-S) and Required Time of Arrival (RTA) control methods during conditions of no error, error in the forecast wind, and offset (disturbance) to the arrival flow. Results indicate that pilots delivered their aircraft to the runway threshold within +/- 3.5 seconds of their assigned arrival time and reported that both the IM-S and RTA procedures were associated with low workload levels. In general, pilots found the IM-S concept, procedures, speeds, and interface acceptable; with 92% of pilots rating the procedures as complete and logical, 218 out of 240 responses agreeing that the IM-S speeds were acceptable, and 63% of pilots reporting that the displays were easy to understand and displayed in appropriate locations. The 22 (out of 240) responses, indicating that the commanded speeds were not acceptable and appropriate occurred during scenarios containing wind error and offset error. Concerns cited included the occurrence of multiple speed changes within a short time period, speed changes required within twenty miles of the runway, and an increase in airspeed followed shortly by a decrease in airspeed. Within this paper, appropriate design recommendations are provided, and the need for continued, iterative human-centered design is discussed.

Swieringa, Kurt↗

NASA NTRS2009

An Exploratory Study of Runway Arrival Procedures: Time Based Arrival and Self-Spacing

The ability of a flight crew to deliver their aircraft to its arrival runway on time is important to the overall efficiency of the National Airspace System (NAS). Over the past several years, the NAS has been stressed almost to its limits resulting in problems such as airport congestion, flight delay, and flight cancellation to reach levels that have never been seen before in the NAS. It is predicted that this situation will worsen by the year 2025, due to an anticipated increase in air traffic operations to one-and-a-half to three times its current level. Improved arrival efficiency, in terms of both capacity and environmental impact, is an important part of improving NAS operations. One way to improve the arrival performance of an aircraft is to enable the flight crew to precisely deliver their aircraft to a specified point at either a specified time or specified interval relative to another aircraft. This gives the flight crew more control to make the necessary adjustments to their aircraft s performance with less tactical control from the controller; it may also decrease the controller s workload. Two approaches to precise time navigation have been proposed: Time-Based Arrivals (e.g., required times of arrival) and Self-Spacing. Time-Based Arrivals make use of an aircraft s Flight Management System (FMS) to deliver the aircraft to the runway threshold at a given time. Self-Spacing enables the flight crew to achieve an ATC assigned spacing goals at the runway threshold relative to another aircraft. The Joint Planning and Development Office (JPDO), a multi-agency initiative established to plan and coordinate the development of the Next Generation Air Transportation System (NextGen), has asked for data for both of these concepts to facilitate future research and development. This paper provides a first look at the delivery performance of these two concepts under various initial and environmental conditions in an air traffic simulation environment.

Houston, Vincent E.↗

NASA NTRS2014

Calculation of Flight Deck Interval Management Assigned Spacing Goals Subject to Multiple Scheduling Constraints

The Federal Aviation Administration's Next Generation Air Transportation System will combine advanced air traffic management technologies, performance-based procedures, and state-of-the-art avionics to maintain efficient operations throughout the entire arrival phase of flight. Flight deck Interval Management (FIM) operations are expected to use sophisticated airborne spacing capabilities to meet precise in-trail spacing from top-of-descent to touchdown. Recent human-in-the-loop simulations by the National Aeronautics and Space Administration have found that selection of the assigned spacing goal using the runway schedule can lead to premature interruptions of the FIM operation during periods of high traffic demand. This study compares three methods for calculating the assigned spacing goal for a FIM operation that is also subject to time-based metering constraints. The particular paradigms investigated include: one based upon the desired runway spacing interval, one based upon the desired meter fix spacing interval, and a composite method that combines both intervals. These three paradigms are evaluated for the primary arrival procedures to Phoenix Sky Harbor International Airport using the entire set of Rapid Update Cycle wind forecasts from 2011. For typical meter fix and runway spacing intervals, the runway- and meter fix-based paradigms exhibit moderate FIM interruption rates due to their inability to consider multiple metering constraints. The addition of larger separation buffers decreases the FIM interruption rate but also significantly reduces the achievable runway throughput. The composite paradigm causes no FIM interruptions, and maintains higher runway throughput more often than the other paradigms. A key implication of the results with respect to time-based metering is that FIM operations using a single assigned spacing goal will not allow reduction of the arrival schedule's excess spacing buffer. Alternative solutions for conducting the FIM operation in a manner more compatible with the arrival schedule are discussed in detail.

ATD-1↗

NASA NTRS2011

A Concept for Flexible Operations and Optimized Traffic into Metroplex Regions

A "Flexible Flight Operations" concept for airport metroplexes was studied. A flexible flight is one whose destination airport is not assigned until a threshold is reached near the arrival area at which time the runway which reduces overall delay is assigned. The concept seeks to increase throughput by exploiting flexibility. The quantification of best-case benefits from the concept was pursued to establish whether concept research is warranted. Findings indicate that indeed the concept has potential for significant reductions in delay (and cost due to delay) in the N90 (NY/NJ) and SCT (Southern California) metroplexes. Delay reductions of nearly 26% are possible in N90 when 30% of the commercial airline flights are flexible (smartly selected by their low probability of connecting passengers); nearly 40% delay reduction is found when 50% of the flights are flexible. In the SCT metroplex, delay reductions estimates are greater. Greater reductions result at SCT since it is less constrained currently than N90, providing "more room" to take advantage of flexibility. Using the flexible operations concept for on-demand/air taxi and General Aviation flights were found to be beneficial at NY/NJ, indicating the flexible operations concepts may be useful to wide variety of users..

DeLaurentis, Daniel↗

NASA NTRS2012

Interval Management with Spacing to Parallel Dependent Runways (IMSPIDR) Experiment and Results

An area in aviation operations that may offer an increase in efficiency is the use of continuous descent arrivals (CDA), especially during dependent parallel runway operations. However, variations in aircraft descent angle and speed can cause inaccuracies in estimated time of arrival calculations, requiring an increase in the size of the buffer between aircraft. This in turn reduces airport throughput and limits the use of CDAs during high-density operations, particularly to dependent parallel runways. The Interval Management with Spacing to Parallel Dependent Runways (IMSPiDR) concept uses a trajectory-based spacing tool onboard the aircraft to achieve by the runway an air traffic control assigned spacing interval behind the previous aircraft. This paper describes the first ever experiment and results of this concept at NASA Langley. Pilots flew CDAs to the Dallas Fort-Worth airport using airspeed calculations from the spacing tool to achieve either a Required Time of Arrival (RTA) or Interval Management (IM) spacing interval at the runway threshold. Results indicate flight crews were able to land aircraft on the runway with a mean of 2 seconds and less than 4 seconds standard deviation of the air traffic control assigned time, even in the presence of forecast wind error and large time delay. Statistically significant differences in delivery precision and number of speed changes as a function of stream position were observed, however, there was no trend to the difference and the error did not increase during the operation. Two areas the flight crew indicated as not acceptable included the additional number of speed changes required during the wind shear event, and issuing an IM clearance via data link while at low altitude. A number of refinements and future spacing algorithm capabilities were also identified.

Baxley, Brian T.↗

NASA NTRS2011

Progress Toward Future Runway Management

The runway is universally acknowledged as a constraining factor to capacity in the National Airspace System (NAS). It follows that investigation of the effective use of runways, both in terms of selection and assignment, is paramount to the efficiency of future NAS operations. The need to address runway management is not a new idea; however, as the complexities of factors affecting runway selection and usage increase, the need for effective research in this area correspondingly increases. Under the National Aeronautics and Space Administration s Airspace Systems Program, runway management is a key research area. To address a future NAS which promises to be a complex landscape of factors and competing interests among users and operators, effective runway management strategies and capabilities are required. This effort has evolved from an assessment of current practices, an understanding of research activities addressing surface and airspace operations, traffic flow management enhancements, among others. This work has yielded significant progress. Systems analysis work indicates that the value of System Oriented Runway Management tools is significantly increased in the metroplex environment over that of the single airport case. Algorithms have been developed to provide runway configuration recommendations for a single airport with multiple runways. A benefits analysis has been conducted that indicates the SORM benefits include supporting traffic growth, cost reduction as a result of system efficiency, NAS optimization from metroplex operations, fairness in aircraft operations, and rational decision making.

Lohr, Gary W.↗

NASA NTRS2019

ATD-2 TFDM Terminal Publication Service (TTP)

Learn the many benefits of the newest SWIM feed from the surface system. This will discuss current options to onboard with this feed, allow participants to ask questions and provide some examples of how the data can be used. Service Includes Flight Data Individual flight updates containing flight identifiers, targeted times, actual times, runway, parking gate, spot, departure fix (predicted, assigned, actual as appropriate), flight states, and more. Airport Information Airport configurations, airport and runway rates, ramp closures, runway closures, taxiway closures. Traffic Management Restrictions Call for Release programs departure MIT/MINIT restrictions, departure stop/ground stop programs. Along with list of impacted flights for each. Flight Delay Airport and runway delay by arrival, departure, and total. Operational Metrics Metrics on airport throughput and individual flight metrics. Surface Metering Program SMP start / end times, metering constraint type / details, updates to existing programs, TMAT compliance window, departure queue length, and more.

Gorman, Shawn M.↗

NASA NTRS1993

Parallel runway requirement analysis study. Volume 2: Simulation manual

This document is a user manual for operating the PLAND_BLUNDER (PLB) simulation program. This simulation is based on two aircraft approaching parallel runways independently and using parallel Instrument Landing System (ILS) equipment during Instrument Meteorological Conditions (IMC). If an aircraft should deviate from its assigned localizer course toward the opposite runway, this constitutes a blunder which could endanger the aircraft on the adjacent path. The worst case scenario would be if the blundering aircraft were unable to recover and continue toward the adjacent runway. PLAND_BLUNDER is a Monte Carlo-type simulation which employs the events and aircraft positioning during such a blunder situation. The model simulates two aircraft performing parallel ILS approaches using Instrument Flight Rules (IFR) or visual procedures. PLB uses a simple movement model and control law in three dimensions (X, Y, Z). The parameters of the simulation inputs and outputs are defined in this document along with a sample of the statistical analysis. This document is the second volume of a two volume set. Volume 1 is a description of the application of the PLB to the analysis of close parallel runway operations.

Ebrahimi, Yaghoob S.↗

NASA NTRS2007

Simulation of Terminal-Area Flight Management System Arrivals with Airborne Spacing

A simulation evaluated the feasibility and potential benefits of using decision support tools to support time-based airborne spacing and merging for aircraft arriving in the terminal area on charted Flight Management System (FMS) routes. Sixteen trials were conducted in each treatment combination of a 2X2 repeated-measures design. In trials 'with ground tools' air traffic controller participants managed traffic using sequencing and spacing tools. In trials 'with air tools' approximately seventy-five percent of aircraft assigned to the primary landing runway were equipped for airborne spacing, including flight simulators flown by commercial pilots. The results indicate that airborne spacing improves spacing accuracy and is feasible for FMS operations and mixed spacing equipage. Controllers and pilots can manage spacing clearances that contain two call signs without difficulty. For best effect, both decision support tools and spacing guidance should exhibit consistently predictable performance, and merging traffic flows should be well coordinated.

Callantine, Todd J.↗

NASA NTRS2018

Air Traffic Management Technology Demostration-1 (ATD-1) Avionics Phase 2 Flight Test and Results

NASA’s first Air Traffic Management Technology Demonstration (ATD-1) subproject successfully completed 19 days of flight test validation in January and February 2017 of an Interval Management (IM) avionics prototype and the procedures used to conduct IM arrival and approach operations. IM is one of the three elements integrated into NASA’s ATD-1 concept of operations with the subproject goal of improving aircraft efficiency and airport throughput during high-density arrival operations. The ATD-1 concept of operations combines advanced arrival scheduling, controller decision support tools, and interval management (IM) avionics to enable merging of multiple, time-based, efficient arrival streams. IM contributes to the operation by calculating speeds that enable an aircraft to precisely achieve a specific time or distance behind another aircraft. When precise spacing intervals can be calculated, achieved, and then maintained during high-density operations, aircraft efficiency should be improved by enabling the aircraft to remain closer to the optimum descent trajectory instead of using vectors and step-down altitudes, and airport throughput should be maintained or improved by each aircraft arriving at the runway threshold closer to the assigned spacing interval. This avionics development and flight test was conducted under a NASA contract by Boeing Research and Technology, with Boeing Commercial Aircraft, Honeywell, United Airlines, and Jeppesen as sub-contractors. The Honeywell built IM avionics were the first ever prototype built based on NASA requirements as well as developing and non-flight tested international IM standards, integrated into two test aircraft, and then flown in real-world conditions at the Grant County International Airport (KMWH). The IM prototype flown in the flight test used data from the Ownship and the assigned lead, or Target, aircraft to calculate the airspeed necessary for the Ownship to achieve the desired spacing. The flight test demonstrated that the IM avionics prototype generally met the IM requirement for spacing accuracy. However, the control laws implemented require further development to reduce the high IM speed command rate and the number of speed reversals observed during the test. Pilots assessed the IM procedure as acceptable, and issues requiring further attention were identified. In summary, the IM avionics prototype showed significant promise in contributing to the goals of improving aircraft efficiency and airport throughput. The flight test results also provided important data to the FAA and the working group developing the follow-on version of the international IM standards.

Baxley, Brian T.↗

NASA NTRSDate not supplied

Applying Machine Learning Tools for Runway Configuration Decision Support

Determining optimal runway configurations at airports, a responsibility assigned to air traffic controllers, is a challenging task. The decision-making process is intricate and involves consideration of many factors such as prevailing wind condition, convective weather, visibility, cloud ceilings, departure and arrival demand, traffic flow, equipment status, and other airport constraints. In a previous work, we developed a Runway Configuration Assistance tool using an offline reinforcement learning method called conservative Q-learning. In this paper, we evaluate and validate our Runway Configuration Assistance tool as a decision support for air traffic controllers. We validated our tool using three airports with differing levels of complexity: Charlotte Douglas International Airport, Denver International Airport, and Dallas Fort Worth International Airport. We quantified the performance of the Runway Configuration Assistance tool based on (1) agreement with historical air traffic controller decisions and (2) violation of decisions that would be obvious to subject-matter experts. Our tool showed promising results in both performance metrics for the three airports, despite the complexities in the runway configuration decision-making process. We also discuss challenges in using machine learning in general to aid air traffic management and identify deployment considerations for the Runway Configuration Assistance tool.

Runway Configuration Management↗

NASA NTRSDate not supplied

Machine Learning Tools for Runway Configuration Decision Support

Runway Configuration Management↗

NASA NTRS2011

Benefit Assessment of the Precision Departure Release Capability Concept

A Precision Departure Release Capability concept is being evaluated by both the National Aeronautics and Space Administration and the Federal Aviation Administration as part of a larger goal of improving throughput, efficiency and capacity in integrated departure, arrival and surface operations. The concept is believed to have the potential of increasing flight efficiency and throughput by avoiding missing assigned slots and minimizing speed increase or path stretch to recover the slot. The main thrust of the paper is determining the impact of early and late departures from the departure runway when an aircraft has a slot assigned either at a meter fix or at the arrival airport. Results reported in the paper are for two scenarios. The first scenario considers flights out of Dallas/Fort Worth destined for Hartsfield-Jackson International Airport in Atlanta flying through the Meridian meter-fix in the Memphis Center with miles-in-trail constraints. The second scenario considers flights destined to George Bush Intercontinental/Houston Airport with specified airport arrival rate constraint. Results show that delay reduction can be achieved by allowing reasonable speed changes in scheduling. It was determined that the traffic volume between Dallas/Fort Worth and Atlanta via the Meridian fix is low and the departures times are spread enough that large departure schedule uncertainty can be tolerated. Flights can depart early or late within 90 minutes without accruing much more delay due to miles-in-trail constraint at the Meridian fix. In the Houston scenario, 808 arrivals from 174 airports were considered. Results show that delay experienced by the 16 Dallas/Fort Worth departures is higher if initial schedules of the remaining 792 flights are kept unaltered while they are rescheduled. Analysis shows that the probability of getting the initially assigned slot back after perturbation and rescheduling decreases with increasing standard deviation of the departure delay distributions. Results show that most Houston arrivals can be expected to be on time based on the assumed zero-mean Normal departure delay distributions achievable by Precision Departure Release Capability. In the current system, airport-departure delay, which is the sum of gate-departure delay and taxi-out delay, is observed at the airports. This delay acts as a bias, which can be reduced by Precision Departure Release Capability.

Palopo, Kee↗

NASA NTRS2014

Functional Analysis for an Integrated Capability of Arrival/Departure/Surface Management with Tactical Runway Management

The runway is a critical resource of any air transport system. It is used for arrivals, departures, and for taxiing aircraft and is universally acknowledged as a constraining factor to capacity for both surface and airspace operations. It follows that investigation of the effective use of runways, both in terms of selection and assignment as well as the timing and sequencing of the traffic is paramount to the efficient traffic flows. Both the German Aerospace Center (DLR) and NASA have developed concepts and tools to improve atomic aspects of coordinated arrival/departure/surface management operations and runway configuration management. In December 2012, NASA entered into a Collaborative Agreement with DLR. Four collaborative work areas were identified, one of which is called "Runway Management." As part of collaborative research in the "Runway Management" area, which is conducted with the DLR Institute of Flight Guidance, located in Braunschweig, the goal is to develop an integrated system comprised of the three DLR tools - arrival, departure, and surface management (collectively referred to as A/D/S-MAN) - and NASA's tactical runway configuration management (TRCM) tool. To achieve this goal, it is critical to prepare a concept of operations (ConOps) detailing how the NASA runway management and DLR arrival, departure, and surface management tools will function together to the benefit of each. To assist with the preparation of the ConOps, the integrated NASA and DLR tools are assessed through a functional analysis method described in this report. The report first provides the highlevel operational environments for air traffic management (ATM) in Germany and in the U.S., and the descriptions of the DLR's A/D/S-MAN and NASA's TRCM tools at the level of details necessary to compliment the purpose of the study. Functional analyses of each tool and a completed functional analysis of an integrated system design are presented next in the report. Future efforts to fully develop the ConOps will include: developing scenarios to fully test environmental, procedural, and data availability assumptions; executing the analysis by a walk-through of the integrated system using these scenarios; defining the appropriate role of operators in terms of their monitoring requirements and decision authority; executing the analysis by a walk-through of the integrated system with operator involvement; characterizing the environmental, system data requirements, and operator role assumptions for the ConOps.

Phojanamongkolkij, Nipa↗

NASA NTRS1997

Departure Trajectory Synthesis and the Intercept Problem

Two areas of the departure problem in air traffic control are discussed. The first topic is the generation of climb-out trajectories to a fix. The trajectories would be utilized by a scheduling algorithm to allocate runways, sequence the proposed departures, and assign a departure time. The second area is concerned with finding horizontal trajectories to merge aircraft from the TRACON to an open slot in the en-route environment. Solutions are presented for the intercept problem for two cases: (1) the aircraft is traveling at the speed of the aircraft in the jetway; (2) the merging aircraft has to accelerate to reach the speed of the aircraft in the en-route stream. An algorithm is given regarding the computation of a solution for the latter case. For the former, a set of equations is given that allows us to numerically solve for the coordinate where the merge will occur.

Bolender, Michael A.↗